Lefschetz number formula for Shimura varieties of Hodge type

For any Shimura variety of Hodge type with hyperspecial level at a prime p and automorphic lisse sheaf on it, we prove a formula, conjectured by Kottwitz {Kottwitz90}, for the Lefschetz numbers of Frobenius-twisted Hecke correspondences acting on the compactly supported \'etale cohomology. Our proof is an adaptation of the arguments of Langlands and Rapoport {LR87} of deriving the Kottwitz's formula from their conjectural description of the set of mod-p points of Shimura variety (Langlands-Rapoport conjecture), which replaces their Galois gerb theoretic arguments by more geometric ones. We also prove a generalization of Honda-Tate theorem in the context of Shimura varieties and fix an error in Kisin's work {Kisin17}. We do not assume that the derived group is simply connected.